The Weyl transform of a compactly supported distribution

Mansi Mishra; M. K. Vemuri

The Weyl transform of a compactly supported distribution

Mansi Mishra, M. K. Vemuri

Abstract

If $T$ is a compactly supported distribution on $\mathbb{R}^{2n}$, then the Weyl transform of $T$ is $p$-power traceable if and only if the Fourier transform of $T$ is $p$-power integrable, and the Weyl transform of $T$ is a compact operator if and only if the Fourier transform of $T$ vanishes at infinity.

The Weyl transform of a compactly supported distribution

Abstract

is a compactly supported distribution on

, then the Weyl transform of

-power traceable if and only if the Fourier transform of

-power integrable, and the Weyl transform of

is a compact operator if and only if the Fourier transform of

vanishes at infinity.

Paper Structure (1 theorem, 21 equations)

This paper contains 1 theorem, 21 equations.

Key Result

Theorem 1

Let $T$ be a compactly supported distribution on ${\mathbb{R}}^{2n}$. Let $\hat{T}$ denote the Fourier transform of $T$. Then $W(T) \in S^p({\mathcal{H}})$ if and only if $\hat{T} \in L^p({\mathbb{R}}^{2n})$ for $1 \leq p \leq \infty$. Moreover, if $K$ is a compact set in ${\mathbb{R}}^{2n}$, then t whenever ${\mathrm{supp}}(T)\subseteq K$. Furthermore, $W(T)$ is compact if and only if $\hat{T}$ v

Theorems & Definitions (1)

Theorem 1